6.1 Gravitational Fields
- a gravitational field exists around objects, describe by the equation F = Gm1m2/d2 (law of universal gravitation), applies to all objects in the solar system (sun, planets, moons, satellites)
- using the law of universal gravitation and newton’s second law, we can determine that the acceleration due to gravity at a distance r from the center of the earth is g = GM/r2, where M is the mass of the earth. (gravity on other planets can be calculated by substituting the appropriate value for M).
6.2 Orbits and Kepler’s Laws
- velocity needed to keep a satellite in orbit around an object with mass M at a radius of r is v = Ö(GM/r)
- Kepler’s first law – each planet moves around the Sun in an orbit that is an ellipse, with the Sun at one focus of the ellipse (although most planets, except for Mercury and Pluto, are almost circular)
- Kepler’s second law – the straight line joining a planet and the Sun sweeps out equal areas in space in equal intervals in time.
- Kepler’s third law – the cube of the average radius r of a planet’s orbit is directly proportional to the square of the period T of the planet’s orbit. r3 = CT2, where C is the constant of proportionality C = GM/(4p2) = r3/T2, where M is the mass of the object being orbited
- Kepler’s laws apply to the motion of any body orbiting another body
6.3 Gravitational Potential Energy in General
- E = mgd is only accurate if g is relatively constant through the vertical displacement, d (a few hundred kilometers from the surface of the earth)
- work done is the area under a force displacement graph for the interval moved
- since F = GMm/r2 then the area under the graph is W = -GMm/r, which is the work to move the object with mass m to a position r away from object with mass M. To get the potential energy (change in energy or work to move from r1 to r2), it is equal to: DE = -GMm/r2 - -GMm/r1
Note: potential energy is referenced to a level of zero at a distance of infinity
- escape from gravitational field: escape energy is the difference between the difference in the potential well on the earth’s surface and potential energy at infinity (i.e. zero), so it is –(-GMm/re). This escape energy will give an escape speed, based on E = ½ m v2
- binding energy is the energy required to go from a certain position to where potential energy = 0 (infinity).
7.1 Electric Charge and Electrical Structure of Matter
- laws of electric charges
- charging by friction
- induced charge separation
- charging by contact
- charging by induction
- the photocopier
7.2 Electric Forces: Coulomb’s Law
- coulomb’s law: the force between two point charges is inversely proportional to the square of the distance between the charges and directly proportional to the product of the charges: F = k q1 q2/ r2, where k is the Coulomb proportionality constant = 9.0 E9 Nm2/C2
- comparing to the law of universal gravitation: forces between charges can be analyzed independently and the result will be the vector sum
7.3 Electric Fields
- field of force: exists in a region of space when an appropriate object placed at a point in the field experiences a force. A small positive test charge is used to determine the direction of the electric field lines around a charge.
- electric field, a vector quantity, is defined as the electric force per unit of positive charge E = FE/q (N / C)
- drawing electric fields
- electric force between parallel plates: practically zero outside the electric plates (except for some bulging around the edges), constant everywhere between the plates, lines are straight, equally spaced, perpendicular to the plates, magnitude of the electric field at any point between the plates (except near the edges) depends only on the magnitude of the charge on the plates, E is proportional to charge per unit area of the plates
- electrostatic precipitators: pollution control devices to remove tiny particles from emissions.
- electric fields in nature
7.4 Electric Potential
- electric potential energy in the system of two charges q1 and q2 is EE = k q1 q2/ r(positive if they repel, negative if the attract).
- 1 volt is the electric potential at a point in an electric field if 1 Joule of work is required to move 1 C of charge from infinity to that point: V = EE / q = (k q1 q / r) / q = k q1 / r ( 1V = 1 J/C)
- electric potential difference: the magnitude of the electric field is the change in potential difference per unit radius E = V/r
- lightning and lightning rods
- medical applications of electric potential
7.5 The Millikan Experiment: Determining the Elementary Charge
- Millikan oil drop experiment showed the smallest unit of charge to be the elementary charge: e = 1.602 E-19 C
7.6 The Motion of Charged Particles in Electric Fields
- a charged particle in a uniform electric field moves with uniform acceleration
- changes to kinetic energy affect potential energy
- cathode ray tube
- inkjet printers
8.1 Natural Magnetism and Electromagnetism
- magnets
- magnetic fields
- earth’s magnetic field
- domain theory of magnetism: ferromagnetic substances are composed of a large number of tiny regions called magnetic domains. Each domain behaves like a tiny bar magnet, with its own N and S poles
- magnetic field of a straight conductor: moving electric charge creates a magnetic field – right hand rule for a straight conductor
- magnetic field of a current loop
- magnetic field of a coil or solenoid – right hand rule for a solenoid
- using electromagnets and solenoids
8.2 Magnetic Force on Moving Charges
- measuring magnetic fields
- a current can exert a force on a magnet and a magnet can exert a force on a current
FM = qvB sin q, where B is the magnitude of the magnetic field, v is the velocity of the particle and q is the charge of the particle, q is the angle between the magnetic field and the velocity (force direction from the right hand rule (palm) or left hand rule)
- charge to mass ratios / cathode ray tube
- effects of magnetic fields
- field theory
8.3 Magnetic Force on a Conductor
- motor principle – right hand rule for the motor principle
- the magnetic force, F, on the conductor is in a direction perpendicular to both the magnitude of the magnetic field B and the direction of the current I: F = I l B sin q
- reversing either the current direction or the magnetic field reverses the direction of the force
8.4 Ampere’s Law
- Along any closed path through a magnetic field, the sum of the products of the scalar component of the magnetic field B, parallel to the path segment with the length of the segment, is directly proportional to the net electric current passing through the area enclosed by the path
- Coaxial cables and magnetic fields
8.5 Electromagnetic Induction
- law of electromagnetic induction: an electric current is induced in a conductor whenever the magnetic field in the region of the conductor changes with time.
- Lenz’s law: when a current is induced in a coil by a changing magnetic field, the electric current is in such a direction that its own magnetic field opposes the change that produced it.
- applying Lenz’s law
- a gravitational field exists around objects, describe by the equation F = Gm1m2/d2 (law of universal gravitation), applies to all objects in the solar system (sun, planets, moons, satellites)
- using the law of universal gravitation and newton’s second law, we can determine that the acceleration due to gravity at a distance r from the center of the earth is g = GM/r2, where M is the mass of the earth. (gravity on other planets can be calculated by substituting the appropriate value for M).
6.2 Orbits and Kepler’s Laws
- velocity needed to keep a satellite in orbit around an object with mass M at a radius of r is v = Ö(GM/r)
- Kepler’s first law – each planet moves around the Sun in an orbit that is an ellipse, with the Sun at one focus of the ellipse (although most planets, except for Mercury and Pluto, are almost circular)
- Kepler’s second law – the straight line joining a planet and the Sun sweeps out equal areas in space in equal intervals in time.
- Kepler’s third law – the cube of the average radius r of a planet’s orbit is directly proportional to the square of the period T of the planet’s orbit. r3 = CT2, where C is the constant of proportionality C = GM/(4p2) = r3/T2, where M is the mass of the object being orbited
- Kepler’s laws apply to the motion of any body orbiting another body
6.3 Gravitational Potential Energy in General
- E = mgd is only accurate if g is relatively constant through the vertical displacement, d (a few hundred kilometers from the surface of the earth)
- work done is the area under a force displacement graph for the interval moved
- since F = GMm/r2 then the area under the graph is W = -GMm/r, which is the work to move the object with mass m to a position r away from object with mass M. To get the potential energy (change in energy or work to move from r1 to r2), it is equal to:
DE = -GMm/r2 - -GMm/r1
Note: potential energy is referenced to a level of zero at a distance of infinity
- escape from gravitational field: escape energy is the difference between the difference in the potential well on the earth’s surface and potential energy at infinity (i.e. zero), so it is –(-GMm/re). This escape energy will give an escape speed, based on E = ½ m v2
- binding energy is the energy required to go from a certain position to where potential energy = 0 (infinity).
7.1 Electric Charge and Electrical Structure of Matter
- laws of electric charges
- charging by friction
- induced charge separation
- charging by contact
- charging by induction
- the photocopier
7.2 Electric Forces: Coulomb’s Law
- coulomb’s law: the force between two point charges is inversely proportional to the square of the distance between the charges and directly proportional to the product of the charges: F = k q1 q2/ r2, where k is the Coulomb proportionality constant = 9.0 E9 Nm2/C2
- comparing to the law of universal gravitation: forces between charges can be analyzed independently and the result will be the vector sum
7.3 Electric Fields
- field of force: exists in a region of space when an appropriate object placed at a point in the field experiences a force. A small positive test charge is used to determine the direction of the electric field lines around a charge.
- electric field, a vector quantity, is defined as the electric force per unit of positive charge E = FE/q (N / C)
- drawing electric fields
- electric force between parallel plates: practically zero outside the electric plates (except for some bulging around the edges), constant everywhere between the plates, lines are straight, equally spaced, perpendicular to the plates, magnitude of the electric field at any point between the plates (except near the edges) depends only on the magnitude of the charge on the plates, E is proportional to charge per unit area of the plates
- electrostatic precipitators: pollution control devices to remove tiny particles from emissions.
- electric fields in nature
7.4 Electric Potential
- electric potential energy in the system of two charges q1 and q2 is EE = k q1 q2/ r (positive if they repel, negative if the attract).
- 1 volt is the electric potential at a point in an electric field if 1 Joule of work is required to move 1 C of charge from infinity to that point: V = EE / q = (k q1 q / r) / q = k q1 / r ( 1V = 1 J/C)
- electric potential difference: the magnitude of the electric field is the change in potential difference per unit radius E = V/r
- lightning and lightning rods
- medical applications of electric potential
7.5 The Millikan Experiment: Determining the Elementary Charge
- Millikan oil drop experiment showed the smallest unit of charge to be the elementary charge: e = 1.602 E-19 C
7.6 The Motion of Charged Particles in Electric Fields
- a charged particle in a uniform electric field moves with uniform acceleration
- changes to kinetic energy affect potential energy
- cathode ray tube
- inkjet printers
8.1 Natural Magnetism and Electromagnetism
- magnets
- magnetic fields
- earth’s magnetic field
- domain theory of magnetism: ferromagnetic substances are composed of a large number of tiny regions called magnetic domains. Each domain behaves like a tiny bar magnet, with its own N and S poles
- magnetic field of a straight conductor: moving electric charge creates a magnetic field – right hand rule for a straight conductor
- magnetic field of a current loop
- magnetic field of a coil or solenoid – right hand rule for a solenoid
- using electromagnets and solenoids
8.2 Magnetic Force on Moving Charges
- measuring magnetic fields
- a current can exert a force on a magnet and a magnet can exert a force on a current
FM = qvB sin q, where B is the magnitude of the magnetic field, v is the velocity of the particle and q is the charge of the particle, q is the angle between the magnetic field and the velocity (force direction from the right hand rule (palm) or left hand rule)
- charge to mass ratios / cathode ray tube
- effects of magnetic fields
- field theory
8.3 Magnetic Force on a Conductor
- motor principle – right hand rule for the motor principle
- the magnetic force, F, on the conductor is in a direction perpendicular to both the magnitude of the magnetic field B and the direction of the current I: F = I l B sin q
- reversing either the current direction or the magnetic field reverses the direction of the force
8.4 Ampere’s Law
- Along any closed path through a magnetic field, the sum of the products of the scalar component of the magnetic field B, parallel to the path segment with the length of the segment, is directly proportional to the net electric current passing through the area enclosed by the path
- Coaxial cables and magnetic fields
8.5 Electromagnetic Induction
- law of electromagnetic induction: an electric current is induced in a conductor whenever the magnetic field in the region of the conductor changes with time.
- Lenz’s law: when a current is induced in a coil by a changing magnetic field, the electric current is in such a direction that its own magnetic field opposes the change that produced it.
- applying Lenz’s law
- technology: ground fault indicator